Question

Assume that the box contains 11 balls: 4 red, 4 blue, and 3 yellow. As in the text, you draw one ball, note its color, and if it is yellow replace it. If it is not yellow you do not replace it. You then draw a second ball and note its color.
(1) What is the probability that the second ball drawn is yellow?

(2) What is the probability that the second ball drawn is red?

Answer 1

1)
$\frac{3}{11} \times \frac{3}{11} + \frac{8}{11} \times \frac{3}{10}= \frac{9}{121}+ \frac{24}{110} =0.29$

2)
$\frac{3}{11} \times \frac{4}{11} +\frac{8}{11} \times \frac{3}{10} +\frac{8}{11} \times \frac{4}{10} = \frac{12}{121}+ \frac{24}{110} + \frac{32}{110} = 0.61$